Recently cluster theory has led to new directions.
Inspired by this,
we study in [1]}, [2]}, [3]} and [4]}
a class of symmetric algebras defined in terms of surface
triangulations, which we call weighted surface algebras. They are periodic as algebras
of period 4 (with a few exceptions).
All but one of the algebras of quaternion type occur in this setting. Furthermore, most algebras of dihedral type, and of semidihedral type
occur naturally as degenerations of these weighted surface algebras. As well, Brauer graph algebras, which includes
blocks of finite type, appear. This places blocks of finite or tame representation
type into a much wider context, which also connects with other parts of mathematics.
